Find the value of p for which the quadratic equation x^2 - px + p+ 3=0 has a) coincident roots - Maths - Complex Numbers and Quadratic Equations

Question

Find the value of p for which the quadratic equation x^2 - px + p+
3=0 has a) coincident roots b) real distinct roots c) one positive
and one negative root Please solve
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Ishwarmani · Accepted Answer

Dear Student, Please find below the solution to the asked query: We have,x2-px+p+3=0a For coincident roots or equal roots,D=0⇒-p2-4p+3=0⇒p2-4p-12=0⇒p2-6p+2p-12=0⇒pp-6+2p-6=0⇒p-6p+2=0⇒p=6 or p=-2b For real distinct roots,D>0⇒-p2-4p+3>0⇒p2-4p-12>0⇒p2-6p+2p-12>0⇒pp-6+2p-6>0⇒p-6p+2>0⇒p>6 or p<-2⇒p∈-∞,-2∪6,∞c For one negative and one positive rootD>0 and 1×f0<0⇒-p2-4p+3>0 and p+3<0⇒p>6 or p<-2 and p<-3 From b⇒p<-3 Regards

Find the value of p for which the quadratic equation x^2 - px + p+ 3=0 has a) coincident roots b) real distinct roots c) one positive and one negative root. Please solve ☺😊😇😄